Question

Consider The polnomial: P(x)=40x^3+116x^2-24x-36.....with one of its zeros being x1=-3. Find the remaining zeros by using synthetic division.
answer choices:
1.x2,3=-1/2,4/5
2.None of these
3.x2,3=-1/4,4/5
4.x2,3=-1/2,3/5
5x2,3=-1/4,3/5
(can someone help me work this out work provided so i can understand this question more in case or future reference? plz and ty ^.^)

Answer 1

x = -3 --> x+3 = 0

So you have to divide P(x) by x+3 to solve for remaining 2 zeros
using synthetic division, put -3 on outside and the coefficients on inside
remember to multiply then add, multiply then add ...

-3| 40 116 -24 -36
-120 12 36
---------------------
40 -4 -12 0

The resulting numbers are the coefficients of the quotient, notice the remainder is zero
P(x) = (x+3)(40x^2 -4x -12) = 0

Solve the quadratic 40x^2 -4x -12 = 0
Divide equation by 4
10x^2 -x -3 = 0
Factor or use quadratic formula
10x^2 +5x -6x -3 = 0
5x(2x +1) -3(2x +1)=0
(2x+1)(5x -3) = 0

2x+1 = 0 --> x = -1/2
5x-3=0 --> x = 3/5